We modify Lemmas 1 and 2 of [1]} to obtain Lemmas REF  and  REF  below. Then we conclude the proof of Theorem REF  by bounding \(E\Bigg [\bigg \lbrace \Xi _{S_*, \pi _*}^{(q)}(H^{(q)},\)  \(A^{(q-1)}, A^{(q)}) - \hat{\Xi }^{(q)}(H^{(q)}, A^{(q-1)}, A^{(q)})\bigg \rbrace ^2\Bigg ]\)  of Lemma REF  using a quantity
\(Err_{\Xi ^{(q+1)}}(\Xi ^{(q)}) = E\bigg \lbrace \max _{a^{(q+1)}} \Xi ^{(q+1)} (H^{(q+1)}, A^{(q+1)}) - \Xi ^{(q)}(H^{(q)}, A^{(q)}) \bigg \rbrace ^2,\) 
